Suwa (諏訪) is a city in Nagano prefecture.
Cheapest way is by bus, from Tokyo or Kyoto. You can also get to Suwa by train from Nagano, first go to Matsumoto and take the Limited Express on the Chuo Train line. The bus station is across the street from the train station on Route 20. It is a small office on the outside of the Plaza.
Check for buses to Suwa sights. There are three local bus routes on those ridiculous looking buses with the quince fruit on the outside. They can take you to Suwakoland, as well as shopping the big stores, and Montbell at Station Park. You can walk to the castle, geyser, and around the downtown area. Trains to neighboring cities. Rent a bicycle at the JR station rental agency. To reach the Yatsugatake, take a train to Chino and then a bus to Minodoguchi.
Soba, bee larvae, raw horse, and fried grasshopper are the local specialties.
There are many izakayas around the station area. Some small local bars in the downtown area. The izakaya in Suwa Plaza across from the station is part of a chain and quite nice.
The best option for a budget traveller is to find a local English teacher and stay with them, or to camp on the west side of the lake, or up the hill behind Suwa near Kirigamine.